Method for determining plasma characteristics

ABSTRACT

Methods for determining characteristics of a plasma are provided. In one embodiment, a method for determining characteristics of a plasma includes obtaining metrics of current and voltage information for first and second waveforms coupled to a plasma at different frequencies, determining at least one characteristic of the plasma using the metrics obtained from each different frequency waveform. In another embodiment, the method includes providing a plasma impedance model of a plasma as a function of frequency, and determining at least one characteristic of a plasma using model. In yet another embodiment, the method includes providing a plasma impedance model of a plasma as a function of frequency, measuring current and voltage for waveforms coupled to the plasma and having at least two different frequencies, and determining ion mass of a plasma from model and the measured current and voltage of the waveforms.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent Ser. No. 11/424,705,filed Jun. 16, 2006, now U.S. Pat. No. 7,286,948 which is herebyincorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to plasma processingtechnologies and, more specifically, to a method for determiningcharacteristics of a plasma in a plasma processing system.

2. Description of the Related Art

Plasma enhanced semiconductor processing chambers are widely used in themanufacture of integrated devices. The process performance generallydepends on the physical, chemical, and electrical properties of theplasma. For example, the uniformity and selectivity of a plasma etchingprocess will be strongly related to the kinetic properties of energeticions of the plasma at or near the surface of a processing substrate. Inan anisotropic etch process, incident ions are made to strike asubstrate surface with a narrow angular velocity distribution that isnearly perpendicular to the surface, thereby providing an ability toetch high aspect ratio features into the substrate. An ion velocitydistribution that is substantially isotropic, however, may result inundesirable etching effects such as bowing or toeing of profile cavitysidewalls.

Furthermore, the kinetic energy distribution of plasma ions may alsoinfluence substrate processing result. Generally, a plasma containschemically reactive species such as atomic radicals (Cl⁻), atomic ions(Cl⁺), molecular ions (Cl₂ ⁺), and excited molecular (Cl₂*), that areproduced by electron-molecule collusions. Plasma generated duringprocessing may have different concentration and/or ratios of atomic ions(Cl⁺) with respect to molecular ions (Cl₂ ⁺). The dynamics of etchingprocesses having different distribution density and/or mixture of atomicand molecular ions (Cl⁺, Cl₂ ⁺) in the plasma may product different etchresults.

Additionally, in plasma etching processes using fluorocarbon gases,released CF_(x) and/or CF_(x)H_(y) from the plasma may redeposit on thesidewall of the etched surface in a process known as sidewallpassivation. Sidewall passivation is utilized to control the sidewallprofile during etching to enable a predetermined depth to be reachedwhile maintaining a desired sidewall profile. However, as the componentand/or ratios of the ions impacting the substrate surface are notcontrolled and/or known in conventional plasma processes, activatedchemical reactions and material sputtered etched from the substratesurface may vary chamber to chamber and even process to process, therebyadversely impacting process control, repeatability and predictability ofthe etch processes.

We have determined that quantitative information about the properties,distribution and energy of ions in a plasma and other plasmacharacteristics will enable meaningful indications of the effectivenessof the process and quality of the process results, thereby enhancingprocess control, repeatability and predictability of the etch processes.We have also determined that the ability to provide plasmacharacteristics enables corresponding improvements in other plasmaprocesses, such as plasma enhanced chemical vapor deposition, physicalvapor deposition, plasma surface treatments, among other plasmaprocesses.

Therefore, there is a need for methods for determining the effective ionenergy and other plasma characteristics that can be used for improvingplasma processes.

SUMMARY OF THE INVENTION

Methods for determining characteristics of a plasma are provided. In oneembodiment, a method for determining characteristics of a plasmaincludes obtaining metrics of current and voltage information of firstand second waveforms coupled to a plasma at different frequencies,determining at least one characteristic of the plasma using the metricsobtained from each different frequency waveform.

In another embodiment, a method for determining characteristics of aplasma includes providing a plasma impedance model of a plasma as afunction of frequency, and determining at least one characteristic of aplasma using model.

In yet another embodiment, a method for determining characteristics of aplasma includes providing a plasma impedance model of a plasma as afunction of frequency, measuring current and voltage for waveformscoupled to the plasma and having at least two different frequencies, anddetermining ion mass of a plasma from model and the measured current andvoltage of the waveforms.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention are attained and can be understood in detail, a moreparticular description of the invention, briefly summarized above, maybe had by reference to the embodiments thereof which are illustrated inthe appended drawings.

FIGS. 1A-C are schematic diagram of exemplary plasma enhanced processingchambers in which embodiments of the invention may be practiced;

FIG. 2 is a process flow diagram of one embodiment of a method fordetermining plasma characteristics; and

FIG. 3 is a simplified circuit diagram of a plasma model.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures. It is contemplated that elements and features of oneembodiment may be beneficially incorporated in other embodiments withoutfurther recitation.

It is to be noted, however, that the appended drawings illustrate onlyexemplary embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

DETAILED DESCRIPTION

Embodiments of the present invention include methods for determiningplasma characteristics using a frequency dependent plasma model. Byanalyzing the plasma at different frequencies, the model facilitatesdetermination of a plurality of plasma characteristics. Some plasmacharacteristics that may be determined include ion mass, distribution ofspecies of the ion mass, ions density, plasma asymmetry, electrontemperature, sheath potential and collision frequency. It iscontemplated that the method may be utilized to determine other plasmacharacteristics.

The plasma characteristics are determined by model analysis usinginformation obtained from RF waveforms coupled to the plasma. In oneembodiment, a first RF waveform used in the model analysis may be usedto sustain the plasma discharge. The second RF waveform used in themodel analysis may also be used to drive the plasma, be a low powerdiagnostic waveform coupled to the plasma, or a waveform harmonic of theplasma. The analysis may also be performed with more than two RFwaveforms coupled to the plasma obtained from other sources, some ofwhich are further described below.

The model takes advantage of the frequency dependence of a plasmadischarge's electrical impedance. The model includes a frequencydependent expression that has plasma characteristics as differentvariables. In practice, a first variable of the model may be solved interms of a second variable in a first model expression representing theplasma state at a first frequency, which can then be substituted intosecond model expression representing the plasma state at a secondfrequency to solve for the second variable. Once a value for the secondvariable has been determined, the value for the second variable may thenbe utilized to determine a value for the first variable.

In the embodiments described herein, the model of the RF waveformanalysis is based on expressions for plasma impedance. Current and/orvoltage are utilized as inputs for solving the expressions in terms ofthe plasma characteristics. It is contemplated that other models may bederived to utilize the methods described herein. It is also contemplatedthat the models may utilize inputs other than, or in addition to,voltage and/or current, such as the phase of the waveform. Although themethods described herein are illustratively presented in terms of anetch application, the methods are equally suitable for use in any plasmaprocesses (i.e., physical vapor deposition, plasma enhanced chemicalvapor deposition, plasma ion implantation and plasma film treatment,among others) for characterizing plasma parameters which can be utilizedto improve process results, prediction and repeatability.

FIGS. 1A-C presents schematic diagrams of plasma processing chambers100A-C in which the present invention may be performed. Examples ofplasma etch chambers that may be adapted to benefit from the presentinclude, but are not limited to, the Decoupled Plasma Source (DPS®, DPS®II), EMAX®, MXP®, and ENABLER® processing chambers, all available fromApplied Material, Inc., of Santa Clara, Calif. It is contemplated thatother plasma chambers, including those from other manufacturers, may beadapted to practice the invention. Although the plasma processingchambers 100A-C illustratively described below is configured as an etchchamber, the invention may be utilized for other plasma processes asindicated above.

Common to all embodiments is at least one RF metrology system 198interfaced with the plasma processing chambers 100A-C which is suitablefor measuring at least one of voltage, current and phase of an RFwaveform coupled to a plasma 110 formed in the chamber from gasesprovided by a gas panel 108. The metrology system 198 may include one ormore sensors. Generally, the metrology system 198 is positioned tointerface with the RF waveform between its source (such as an RF powersource, or the plasma itself).

Referring now to FIG. 1A, the plasma processing chamber 100A includes agrounded chamber body 102 coupled to the gas panel 108, one or more RFpower sources and a controller 190. The gas panel 108 provides processand other gases to the process region defined in the chamber body 102.At least one of the RF power sources is utilized to sustain the plasma110 formed from the process gases within the process region, typicallyto promote substrate processing, chamber or component seasoning and/orcoating, and/or chamber cleaning.

A substrate support pedestal 116 disposed within the chamber body 102below a gas distributor 132. The pedestal 116 may include anelectrostatic chuck (not shown) for retaining a substrate 114 below thegas distributor 132. The electrostatic chuck is driven by a DC powersupply to develop an electrostatic force that holds the substrate 114 tothe chuck surface, as is conventionally known. Alternatively, thesubstrate 114 may be retained to the pedestal by clamping, vacuum orgravity.

In one embodiment, the substrate support pedestal 116 is configured as acathode and is coupled to a plurality of RF power sources. RF power,provided by at least a first RF power source 104, is coupled between thecathode and another electrode, such as the gas distributor 132 orceiling of the chamber body 102. The RF power excites and sustains aplasma discharge (e.g., plasma 110) formed from the gases disposed inthe processing region of the chamber body 102.

In the embodiment depicted in FIG. 1A, a plurality of RF power sources104, 106 are coupled to the cathode through a matching circuit 112.Although not as depicted in FIG. 1A, the matching circuit 112 mayincorporate or interface with the RF metrology system 198. The signalgenerated by the RF power sources 104, 106 is delivered through matchingcircuit 112 to the substrate support pedestal 116 through a single feedforming to ionize the background gas mixture provided in the plasmaprocessing chamber 100A, thereby providing ion energy necessary forperforming an etching or other plasma enhanced process. The RF powersources 104, 106 are generally capable of producing an RF signal havinga frequency of from about 50 kHz to about 200 MHz and a power betweenabout 0 Watts and about 5000 Watts. Another optional RF source 120 isshown in FIG. 1A and is representative of one or more additional powersources that may be used to control the characteristics of the plasma110.

The gas distributor 132 may comprise one or more nozzles or ashowerhead. The gas distributor 132 is coupled to the gas panel 108 suchthat gases provided to the gas distributor 132 from the gas panel 108may introduced into the chamber and, when ignited, formed into theplasma 110 utilized for processing the substrate 114.

In one mode of operation, the substrate 114 is disposed on the substratesupport pedestal 116 in the plasma processing chamber 100. A process gasand/or gas mixture is introduced into the chamber body 102 through thegas distributor 132 from the gas panel 108. A vacuum pumping system 122maintains the pressure inside the chamber body 102 while removing etchby-products. The vacuum pumping system 122 typically maintains anoperating pressure between about 10 mTorr to about 20 Torr.

The RF source 104, 106 provides RF power at separate frequencies to thecathode through the matching circuit 112, thereby providing energy toform the plasma 110 and excite the gas mixture in the chamber body 102into ions to perform a plasma process, in this example, an etchingprocess. The RF metrology system 198 measures metrics of the waveformcoupled to the plasma 110 to provide a metric indicative of the powerprovided by each power source 104, 106. The metric is transmitted to thecontroller 190 and utilized to determine characteristics of the plasmaas further detailed below. The characteristics of the plasma may beanalyzed to adjust the process in-situ processing, to correct processdrift, to match processes between different chambers, and/or to achievecertain process results.

The controller 190 is coupled to the various components of the plasmaprocessing chamber 100 and is used to facilitate control of an etchprocess. The controller 190 generally includes a central processing unit(CPU) 192, a memory 194, and support circuits 196 for the CPU 192. TheCPU 192 may be one of any form of computer processor that can be used inan industrial setting for controlling various chambers andsubprocessors. The memory 194 is coupled to the CPU 192. The memory 194,or computer-readable medium, may be one or more of readily availablememory such as random access memory (RAM), read only memory (ROM),floppy disk, hard disk, or any other form of digital storage, local orremote. The support circuits 196 are coupled to the CPU 192 forsupporting the processor in a conventional manner. These circuitsinclude cache, power supplies, clock circuits, input/output circuitryand subsystems, and the like.

A process, for example a method 200 for determining plasmacharacteristics described below, is generally stored in the memory 194,typically as a software routine. The software routine may also be storedand/or executed by a second CPU (not shown) that is remotely locatedfrom the hardware being controlled by the CPU 192. Although the processof the present invention is discussed as being implemented as a softwareroutine, some of the method steps that are disclosed therein may beperformed in hardware as well as by the software controller. As such,the invention may be implemented in software as executed upon a computersystem, in hardware as an application specific integrated circuit orother type of hardware implementation, or a combination of software andhardware.

FIG. 1B depicts another embodiment of a plasma processing chamber 100Bin which the present invention may be performed. The plasma processingchamber 100B is substantially similar to the plasma processing chamber100A described above, and a low power diagnostic power source 130 iscoupled to the plasma 110. The processing chamber 100B may utilize asingle RF source 104 to sustain the plasma 110, or alternatively otheroptional RF power sources 120 may be additionally utilized. Themetrology system 198 is configured to obtain a metric of at least one ofcurrent, voltage and phase from both the low power RF diagnostic powersource 130 and the RF power source 104.

The low power RF diagnostic power source 130 is coupled to the plasma atfrequency different that of the power provided by the primary or plasmaRF source 104. The diagnostic power only serves as a source ofadditional frequency information for plasma impedance measurement, anddoes not significantly change the operational characteristics of theplasma discharge. In one embodiment, the diagnostic power form thesource 130 is provides between about 10 milliwatts to about 10 Watts tothe plasma.

FIG. 1C depicts another embodiment of a plasma processing chamber 100Cin which the present invention may be performed. The plasma processingchamber 100C is substantially similar to the plasma processing chambers100A-B described above, except wherein the metrology system 198 isconfigured for measuring one or more RF waveforms that are harmonics ofthe plasma, i.e., the plasma serves as a source of the waveform, as wellas waveforms from the RF source 104. The metrology system 198 isgenerally disposed between a circuit element 140 and the plasma 110. Thecircuit element 140, such as a low pass filter, is selected to create anopen circuit for waveforms having a frequency greater than thefundamental frequency (i.e., the frequency provided by the RF source104), thereby protecting the RF sources from reflected plasma harmonics.

The plasma 110 formed in the chamber 100C may be sustained by a singleRF source 104, or alternatively other optional RF power sources 120 maybe additionally utilized. It is contemplated that a low power diagnosticpower source 130 (as shown in FIG. 1B, may also be coupled to thechamber 100C.

FIG. 2 depicts a process flow diagram of one embodiment of a method 200for determining characteristics of the plasma 110 that may be performedin the plasma processing chambers 100A-C using information obtained bythe RF metrology system 198. For sake of clarity, plasma processingchambers 100A-C will be collectively referred henceforth as “the plasmaprocessing chambers” without further the reference to the numerals100A-C.

The method 200 begins at step 202 by placing the substrate 114 on thesupport pedestal 116 disposed in the plasma processing chamber. It isnoted that the method 200 may be performed without a substrate withinthe chamber.

At step 204, one or more process gases are supplied from the gas panel108 into the plasma processing chamber and are formed into the plasma110 to provide reactive species (e.g., ions or radicals) used forprocessing. At step 206, power is provide from one or more RF powersources to sustain the plasma 110.

At step 208, the metrology system 198 obtains metrics indicative of theRF waveforms coupled to the plasma 110. In one embodiment, the RFwaveforms are from the RF sources 104, 106 which provide power atdifferent frequencies to sustain the plasma, as shown in FIG. 1A. Somecommon frequencies pairs include 2 and 13 kHz, 2 and 60 kHz, and 13 and60 kHz. In embodiments where three RF power sources are used to sustainthe plasma, common frequencies groupings include 2, 13 and 60 kHz and 2,13 and 162 kHz.

In another embodiment, one of the RF waveforms is from a first RF sourceutilized to provide power sustain the plasma, while another RF waveformis from a second RF source that generates a low power diagnostic powerthat is coupled to the plasma at different frequency different that thepower provided by the first RF source, as shown in FIG. 1B. It is alsocontemplated that multiple low power diagnostic power sources may beutilized to generate the different waveforms. The diagnostic waveformsmay be used alone, or in conjunction with the waveforms obtained fromother sources.

In yet another embodiment, one of the RF waveforms is from a first RFsource utilized to provide power sustain the plasma, while another RFwaveform is a harmonic of the plasma, i.e., the plasma serves as asource of the second frequency waveform which is at a frequencydifferent that the power provided by the first RF source, as shown inFIG. 1C. It is also contemplated that waveforms from more than oneharmonic frequency may be utilized. The harmonic waveforms may be usedalone, or in conjunction with the waveforms obtained from other sources.

It is contemplated that waveforms forms difference frequencies may beobtained by any combination of the examples given above. For example,one or more RF sustaining waveforms (at one or more frequencies) may beanalyzed with waveforms obtained from harmonic and/or diagnosticsources. In another example, one or more harmonic waveforms may beanalyzed with waveforms obtained from one or more diagnostic RF sources.

In one embodiment, the metrology system 198 is utilized to obtaincurrent and voltage metrics of RF waveforms measured between the sourceand plasma. The metrics are provided to the controller 190.

At step 210, the controller 190 determines two or more characteristicsof the plasma utilizing the metrics provided form the metrology system198. In one embodiment, the metrics are utilized by the controller 190to determine sheath voltage and ion density. The sheath voltage isapproximately equal to the amplitude of the RF voltage modulation, whilethe ion density if approximately equal to the magnitude of the RFcurrent. The sheath voltage and ion density are utilized as inputvariables for a model that expresses the plasma impedance as a functionof frequency.

The model is generally a lump element circuit expression of the plasmausing known electrical plasma characteristics. For example, the portionof the expression for sheath impedance may be based on Childs Law, whilethe portion of the expression for bulk impedance may be based onhomogeneous plasma models. It is contemplated that the model may bebased on other theories or derived empirically, and resolved to obtainplasma characteristics utilizing the method described herein.

The model generally includes variables for ion mass, collisionfrequency, electron temperature, plasma asymmetry, sheath voltage andion density. As values for ion density and sheath voltage are providedas discussed above, the expression of the model may be resolved for anyof the remaining variables, e.g., ion mass, collision frequency,electron temperature and plasma asymmetry. If waveform information isavailable at only two frequencies, two of the four remaining variablesmay be assigned approximated values so that the other variables ofgreater interest may be resolved. If waveform information is availableat three or more frequencies, all of the four remaining variables may bedetermined.

The model is utilized by solving for a first variable using a modelexpression at a first frequency, than substituting the first variable,expressed in terms of the first frequency model expression, into themodel expression for the second frequency, wherein a second variable ofinterest may be resolved. Using the resolve value of the secondvariable, the valve for the first variable may be resolve. Utilizingthis method, any pair of ion mass, collision frequency, electrontemperature and plasma asymmetry may be determined using two frequencymodel analysis, or all may be determined using model analysis at threeor more frequencies. It is contemplated that the model may be resolvedusing other analytical approaches, for example, neural networks, bestfit, regression analysis, solving for a unique solution for allequations, among others

FIG. 3 is one embodiment of a simplified circuit diagram of a plasmamodel. The plasma model may assume an asymmetric capacitive discharge(homogeneous, constant ion MFP) using high frequency bulk plasmaapproximation (see, for example, Godyak V 1986 Soviet RF DischargeResearch and Child Law High Voltage Sheath Approximation (C. D. Child,Phys. Rev., 32)). In an illustrative embodiment, an Argon plasma mayhave center point parameters of n_(e)=1010 cm⁻³, V_(DC)=500 Volts,ν_(me)=0.01/ns, α=0.5, and T_(e)=5 eV.

The sheath reactance may be expressed as:

$J_{d} = \frac{\omega \cdot ɛ_{0} \cdot V}{s}$$I_{d} = {\frac{\omega \cdot ɛ_{0} \cdot V \cdot {Area}}{s_{0}} = {\omega \cdot C_{sheath} \cdot V}}$$C_{sheath} = \frac{ɛ_{0} \cdot {Area}}{s}$Sheath thickness can be approximated by

$s = \sqrt[4]{\frac{32 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3}}{81 \cdot {.372} \cdot n_{e}^{2} \cdot e \cdot T_{e}}}$$\frac{1}{s} = \sqrt[4]{\frac{81 \cdot 0.61 \cdot n_{e}^{2} \cdot e \cdot T_{e}}{32 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3}}}$$C_{sheath} = \frac{ɛ_{0} \cdot {Area}}{s}$$X_{sheath} = \frac{- s}{\omega \cdot ɛ_{0} \cdot {Area}}$$X_{sheath} = {\frac{- 1}{\omega \cdot ɛ_{0\;} \cdot {Area}} \cdot \sqrt[4]{\frac{32 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3}}{81 \cdot {.372} \cdot n_{e}^{2} \cdot e \cdot T_{e}}}}$

The sheath resistance may be expressed as:

$J_{i} = {{\frac{2 \cdot \omega_{i}}{3 \cdot \pi \cdot \omega} \cdot J_{d}} = \frac{2 \cdot \omega_{i} \cdot ɛ_{0} \cdot V}{3 \cdot \pi \cdot s}}$J_(i) = J_(e)$J_{c} = {{J_{i} + J_{e}} = {{2 \cdot J_{i}} = \frac{4 \cdot \omega_{i} \cdot ɛ_{0} \cdot V}{3 \cdot \pi \cdot s}}}$$R_{sheath} = {\frac{V}{J_{c} \cdot {Area}} = \frac{3 \cdot \pi \cdot s}{4 \cdot \omega_{i} \cdot ɛ_{0} \cdot {Area}}}$$\omega_{i} = {\pi \cdot \omega_{pi} \cdot \sqrt[4]{\frac{2 \cdot T_{e}}{e \cdot V_{D\; C}}}}$$R_{sheath} = {\frac{3 \cdot s}{4 \cdot \omega_{pi} \cdot ɛ_{0} \cdot {Area}} \cdot \sqrt[4]{\frac{e \cdot V_{D\; C}}{2 \cdot T_{e}}}}$$\omega_{pi} = {e\sqrt{\frac{n_{e}}{ɛ_{0} \cdot M}}}$$R_{sheath} = {\frac{3 \cdot s}{4 \cdot e \cdot ɛ_{0} \cdot {Area}} \cdot \sqrt[4]{\frac{e \cdot V_{D\; C} \cdot ɛ_{0}^{2} \cdot M^{2}}{2 \cdot T_{e} \cdot n_{e}^{2}}}}$$R_{sheath} = {\frac{3 \cdot V_{D\; C}}{2 \cdot e \cdot n_{e} \cdot {Area}} \cdot \sqrt[4]{\frac{M^{2}}{T_{e}^{2} \cdot 81 \cdot 0.372}}}$

Treating as parallel elements, starting with the powered sheath, andscaling the grounded sheath due to asymmetry conditions:

$R_{shRF} = \frac{\frac{2}{9 \cdot \omega^{2} \cdot ɛ_{0} \cdot e \cdot {Area} \cdot n_{e} \cdot T_{e}} \cdot \sqrt{\frac{2 \cdot V_{D\; C}^{3} \cdot M}{0.61 \cdot e}}}{{\frac{4}{9 \cdot \omega^{2} \cdot ɛ_{0}} \cdot \sqrt{\frac{2 \cdot V_{D\; C}}{e \cdot T_{e}}}} + \frac{V_{D\; C} \cdot M}{4 \cdot e^{2} \cdot n_{e} \cdot T_{e}}}$$X_{shRF} = \frac{\frac{{- V_{D\; C}} \cdot M}{2 \cdot e^{2} \cdot n_{e} \cdot T_{e} \cdot \omega \cdot ɛ_{0} \cdot {Area}} \cdot \sqrt[4]{\frac{2 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3}}{81 \cdot {.372} \cdot n_{e}^{2} \cdot e \cdot T_{e}}}}{{\frac{4}{9 \cdot \omega^{2} \cdot ɛ_{0}} \cdot \sqrt{\frac{2 \cdot V_{D\; C}}{e \cdot T_{e}}}} + \frac{V_{D\; C} \cdot M}{4 \cdot e^{2} \cdot n_{e} \cdot T_{e}}}$$\frac{V_{GND}}{V_{RF}} = \left( \frac{Area}{{Area}_{GND}} \right)^{q}$$\alpha = \frac{Area}{{Area}_{GND}}$ V_(GND) = V_(D C)α^(q)$R_{shGND} = \frac{\frac{2}{9 \cdot \omega^{2} \cdot ɛ_{0} \cdot e \cdot {Area} \cdot n_{e} \cdot T_{e}} \cdot \sqrt{\frac{2 \cdot V_{D\; C}^{3} \cdot \alpha^{3 \cdot q} \cdot M}{0.61 \cdot e}}}{{\frac{4}{9 \cdot \omega^{2} \cdot ɛ_{0}} \cdot \sqrt{\frac{2 \cdot V_{D\; C} \cdot \alpha^{q}}{e \cdot T_{e}}}} + \frac{V_{D\; C} \cdot \alpha^{q} \cdot M}{4 \cdot e^{2} \cdot n_{e} \cdot T_{e}}}$$X_{shGND} = \frac{\frac{{- V_{D\; C}} \cdot \alpha^{q} \cdot M}{2 \cdot e^{2} \cdot n_{e} \cdot T_{e} \cdot \omega \cdot ɛ_{0} \cdot {Area}} \cdot \sqrt[4]{\frac{2 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3} \cdot \alpha^{3 \cdot q}}{81 \cdot {.372} \cdot n_{e}^{2} \cdot e \cdot T_{e}}}}{{\frac{4}{9 \cdot \omega^{2} \cdot ɛ_{0}} \cdot \sqrt{\frac{2 \cdot V_{D\; C} \cdot \alpha^{q}}{e \cdot T_{e}}}} + \frac{V_{D\; C} \cdot \alpha^{q} \cdot M}{4 \cdot e^{2} \cdot n_{e} \cdot T_{e}}}$

The bulk impedance may be expressed as Z_(bulk), and thus the totaldischarge impedance verses n_(e), V_(DC), ν_(me), α, M_(ion) and T_(e)may be expressed as:

$Z_{bulk} = \left( {{i \cdot \omega \cdot C_{0}} + \frac{1}{{i \cdot \omega \cdot L_{p}} + R_{p}}} \right)^{- 1}$$L_{p} = \frac{1}{\omega_{pe}^{2} \cdot C_{0}}$$R_{p} = \frac{v_{me}}{\omega_{pe}^{2} \cdot C_{0}}$$Z_{bulk} = \left( {{i \cdot \omega \cdot C_{0}} + \frac{\omega_{pe}^{2} \cdot C_{0}}{{i \cdot \omega} + v_{me}}} \right)^{- 1}$$C_{0} = \frac{ɛ_{0} \cdot {Area} \cdot \left( {1 + \alpha} \right)}{L - {s_{0} \cdot \left( {1 + \frac{1}{\frac{q}{\alpha^{2}}}} \right)}}$$s = \sqrt[4]{\frac{32 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3}}{81 \cdot {.372} \cdot n_{e}^{2} \cdot e \cdot T_{e}}}$$C_{0} = \frac{ɛ_{0} \cdot {Area} \cdot \left( {1 + \alpha} \right)}{L - {\sqrt[4]{\frac{32 \cdot ɛ_{0}^{2} \cdot V_{D\; C}^{3}}{81 \cdot {.372} \cdot n_{e}^{2} \cdot e \cdot T_{e}}} \cdot \left( {1 + \frac{1}{\frac{q}{\alpha^{2}}}} \right)}}$where n_(e), V_(DC), ν_(me), α, M_(ion) and T_(e) respectively areelectron density, sheath voltage, collision frequency, dischargeasymmetry, ion mass and electron temperature.

Therefore, by measuring the impedance of the equivalent circuit atfrequencies 1, 2, . . . n and relating the circuit elements C_(shGND),R_(shGND), C₀, R_(p), L_(p), C_(shRF), and R_(shRF) to plasma parametersn_(e), V_(DC), ν_(me), α, m_(ion), and T_(e) using the equations above,the plasma parameters can be directly determined from impedancemeasurement.

The plasma characteristics determined at step 210 may be utilized todetermine the energy of the effective ions mass generated by the plasmaas calculated in accordance with the simulated voltage and currentmagnitudes obtained by the simulated models. Plasma characteristics, forexample ion mass determined at step 210, may also be utilized to resolvethe distribution of ions and species within a plasma. As thedissociation of the gas mixture in the processing chamber may be ionizedwith different forms, such as atomic radicals (Cl·), atomic ions (Cl⁺),molecular ions (Cl₂ ⁺) and excited molecular (Cl₂*), an accuratedetermination of the distribution of the ions species within the plasmamay be utilized to more effectively control plasma processing. Thedistribution of species may be resolved for either atomic and/ormolecular distributions. For example, atomic radicals (Cl·) and/oratomic ions (Cl⁺) may be recombined and formed as molecular ions (Cl₂ ⁺)instead of reacting with the material (e.g., SiO₂ or metal) on thesubstrate, thereby adversely influencing the process performance asdesired and alternating the ions distributed in the process region. Byknowing the ion mass and resolving the ion distribution for a particularset of process parameters, process performance may more accurately beestimated without lengthy process characterization. As such, theestimation of the effective ion energy and/or distribution may becalculated by the voltage and current magnitudes of RF waveforms coupledto the plasma, thereby identifying the actual reactive species remainedand generated in the process chamber. As such, the invention isparticularly useful for determining the molecular and atom distributionsof diatomic gases (for example, Cl₂, O₂ and N₂, among others) within theplasma. The invention is also useful for determining the distributionsof compound fragments within the plasma, such as the distribution of CF₄process gas fragments (CF⁺³, CF₂ ⁺², etc). Thus, the process will allowimmediate identification of process drift or variations between items,such as process kit variation, chamber to chamber variation and evenvariation in the composition of gas sources (of a process gas).

Thus, the present application provides methods determining plasmacharacteristics using a frequency dependant, plasma model. By analyzingthe plasma at different frequencies, the model facilitates determinationof plasma characteristics such as ion mass, the distribution of ion massspecies, ions density, plasma asymmetry, electron temperature, sheathpotential and collision frequency. As a result, the methodsadvantageously facilitate enhanced process control, management andrepeatability of plasma processes.

While the foregoing is directed to embodiments of the present invention,other and further embodiments of the invention may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

1. A method for determining characteristics of a plasma, comprising:providing a plasma impedance model of a plasma as a function offrequency; measuring a metric of a plasma harmonic waveform from theplasma; storing the measured harmonic waveform information in a storagedevice; determining at least one characteristic of a plasma using model;adjusting processing parameters based on the at least one characteristicof the plasma to obtain a predetermined plasma characteristic; andprocessing a substrate in the presence of a plasma having thepredetermined plasma characteristic.
 2. The method of claim 1, whereinthe step of determining further comprises: obtaining current and voltageinformation of RF waveforms having different frequencies that arecoupled to the plasma.
 3. The method of claim 2, wherein the step ofobtaining further comprises: measuring metrics of waveforms provided bya plurality of RF power sources utilized to sustain the plasma.
 4. Themethod of claim 1, wherein the step of determining further comprises:determining at least one of an ion mass of the plasma, a distribution ofion mass species within the plasma, an asymmetry of the plasma, anelectron temperature of the plasma or an electron-molecule collisionfrequency within the plasma.
 5. The method of claim 1, wherein the stepof determining further comprises: determining a distribution betweenchlorine (Cl) species within the plasma.
 6. The method of claim 1,wherein the step of determining further comprises: monitoring the atleast one characteristic for drift.
 7. The method of claim 1, whereinthe step of determining further comprises: monitoring the ion mass fordrift during processing.
 8. A method for determining characteristics ofa plasma, comprising: providing a plasma impedance model of a plasma asa function of frequency; measuring current and voltage for waveformscoupled to the plasma and having at least two different frequencies;measuring a metric of waveform provided by a low power diagnostic sourcethat does not significantly change an operational characteristic of theplasma; storing the measured current and voltage information in astorage device; and determining ion mass of a plasma from model and themeasured current and voltage of the waveforms.
 9. The method of claim 8,wherein the step of determining further comprises: determining anelectron-molecule collision frequency within the plasma from model andthe measured current and voltage of the waveforms.
 10. The method ofclaim 8, wherein the step of measuring further comprises: measuringmetrics of waveforms provided by a plurality of RF power sourcesutilized to sustain the plasma.
 11. The method of claim 8, wherein thestep of determining further comprises: determining a distributionbetween diatomic species within the plasma.
 12. The method of claim 8,wherein the step of determining further comprises: determining adistribution between process gas fragments within the plasma.
 13. Themethod of claim 8 further comprising: adjusting processing parametersbased on the determined ion mass to obtain a target ion mass; andprocessing a substrate in the presence of a plasma having the target ionmass.